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Is there any physical or scientific significance for the fact that an inscribed sphere in a regular tetrahedron have exactly the same surface to volume ratio at any size?, (i.e. does it have any use or applications?)

SdogV
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    Could you perhaps link to the result you're mentioning? – Bob Knighton Jan 04 '19 at 21:00
  • That cannot be right. Volume goes as $L^3$ while area goes as $L^2$, so surface to volume should go as $1/L$ – Gabriel Golfetti Jan 04 '19 at 22:29
  • @Gabriel Golfetti: The question doesn't claim that the surface to volume ratio is the same at all sizes, but rather that the ratios for the tetrahedron & the inscribed sphere are the same as each other's at all sizes. – D. Halsey Jan 05 '19 at 01:06
  • The Wikipedia page on tetrahedrons gives formulas for the surface area, the volume, and the radius of the inscribed sphere. Using these, it's easy to show that what's claimed in the question is, in fact, true. But I've got no clue as to the significance or use of the fact. – D. Halsey Jan 05 '19 at 01:11
  • Since you agree that it is possible for the inscribed sphere and regular tetrahedron can have equal surface to volume ratios might that ratio represent an "activity" which would than imply that thermostaedic equilibrium is satisfied at this condition for "spaces" of spheres and regular tetrahedrons?? (i.e when edge to sphere ratios are near 4.9!?) – SdogV Jan 07 '19 at 18:17
  • AND the inscribed tetrahedron in a sphere represents a more active "activity"!! ( I if anyone is really interested, I may be contacted directly at terikson@IIT.edu ) – SdogV Jan 07 '19 at 18:21

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